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Mirrors > Home > MPE Home > Th. List > ceqsex4v | Structured version Visualization version Unicode version |
Description: Elimination of four existential quantifiers, using implicit substitution. (Contributed by NM, 23-Sep-2011.) |
Ref | Expression |
---|---|
ceqsex4v.1 | |
ceqsex4v.2 | |
ceqsex4v.3 | |
ceqsex4v.4 | |
ceqsex4v.7 | |
ceqsex4v.8 | |
ceqsex4v.9 | |
ceqsex4v.10 |
Ref | Expression |
---|---|
ceqsex4v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.42vv 1920 | . . . 4 | |
2 | 3anass 1042 | . . . . . 6 | |
3 | df-3an 1039 | . . . . . . 7 | |
4 | 3 | anbi2i 730 | . . . . . 6 |
5 | 2, 4 | bitr4i 267 | . . . . 5 |
6 | 5 | 2exbii 1775 | . . . 4 |
7 | df-3an 1039 | . . . 4 | |
8 | 1, 6, 7 | 3bitr4i 292 | . . 3 |
9 | 8 | 2exbii 1775 | . 2 |
10 | ceqsex4v.1 | . . 3 | |
11 | ceqsex4v.2 | . . 3 | |
12 | ceqsex4v.7 | . . . . 5 | |
13 | 12 | 3anbi3d 1405 | . . . 4 |
14 | 13 | 2exbidv 1852 | . . 3 |
15 | ceqsex4v.8 | . . . . 5 | |
16 | 15 | 3anbi3d 1405 | . . . 4 |
17 | 16 | 2exbidv 1852 | . . 3 |
18 | 10, 11, 14, 17 | ceqsex2v 3245 | . 2 |
19 | ceqsex4v.3 | . . 3 | |
20 | ceqsex4v.4 | . . 3 | |
21 | ceqsex4v.9 | . . 3 | |
22 | ceqsex4v.10 | . . 3 | |
23 | 19, 20, 21, 22 | ceqsex2v 3245 | . 2 |
24 | 9, 18, 23 | 3bitri 286 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wex 1704 wcel 1990 cvv 3200 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: ceqsex8v 3249 dihopelvalcpre 36537 |
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